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DETERMINATION OF ASPARTAME IN SOFT DRINKS USING HPLC BACHELOR OF CHEMICAL ENGINEERING FACULTY OF ENGINEERING - UNIVERSITY OF SOUTHERN DENMARK SPRING 2012 Mohammad Adnan Hajjaj Morten Gildsig Poulsen Morten Hjort Løvendahl Nielsen Juan Viamonte Dominguez Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 2 of 2 TABLE OF CONTENTS FIGURE LIST p.5 TABLE LIST p.7 RESUME p.8 ABSTRACT p.9 PREFACE p.10 1. INTRODUCTION p.11 1.1. PROBLEM STATEMENT p.11 1.1.1. Introduction p.11 1.1.2. The aim of the project p.11 1.1.3. Hypothesis p.11 1.1.4. Reason for using HPLC p.12 1.1.5. The analysis p.12 1.1.6. Method 1 p.12 1.1.7. Method 2 p.12 1.2. BACKGROUND p.13 1.2.1. History of aspartame p.13 1.2.2. Characteristics and properties of aspartame p.14 1.3. OBJECTIVES OF STUDY p.16 1.4. LEGISLATION p.16 2. HPLC THEORY p.18 2.1. ADVANTAGES AND DISADVANTAGES p.18 2.2. HPLC DEVICE p.18 2.3. SEPARATION MODES p.20 2.4. RETENTION TIME & VOID TIME p.21 2.5. VOLUMES p.22 2.6. RETENTION FACTOR & PARTITION COEFICIENT p.22 2.7. SELECTIVITY & SOLVENT STRENGTH p.23 2.8. BUFFERS p.24 2.9. COLUMN EFFICIENCY & NUMBER OF PLATES p.25 2.10. HETP (Height equivalent to a theorical plate) p.25 2.11. RESOLUTION & PEAK SYMMETRY p.25 2.12. ISOCRATIC & GRADIENT FLOW p.28 2.13. PEAK CAPACITY p.28 Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 3 of 3 3. STATISTICAL THEORY p.30 3.1. INTRODUCTION p.30 3.2. THE NORMAL DISTRIBUTION p.30 3.3. t-DISTRIBUTION p.33 3.4. F-DISTRIBUTION p.34 3.5. CONFIDENCE INTERVAL p.35 3.6. HYPOTHESIS TESTING p.36 3.7. LINEAR REGRESSION p.40 3.8. BOXPLOTS p.44 3.9. Q-TEST p.44 3.10. ANALYSIS OF VARIANCE (ANOVA) p.45 4. METHOD VALIDATION THEORY p.47 4.1. SPECIFICITY p.47 4.2. RANGE p.47 4.3. LINEARITY p.47 4.4. PRECISION p.48 4.5. ACCURACY p.48 4.6. LIMIT OF DETECTION (LOD) p.49 4.7. LIMIT OF QUANTIFICATION (LOQ) p.49 4.8. RUGGEDNESS p.49 5. METHOD OPTIMIZATION p.50 5.1. INITIAL METHOD p.50 5.2. NEW METHOD p.51 5.3. OPTIMIZED METHOD p.52 5.4. OPTIMIZATION RESULTS p.53 6. DESCRIPTION OF EXPERIMENTAL WORK p.54 6.1. CHROMATOGRAMS p.54 6.2. MATERIALS p.55 6.3. METHOD DESCRIPTION p.57 6.3.1. Samples p.58 6.3.2. Reagents p.59 6.3.3. Dilution water p.59 6.3.4. Stock solution p.59 6.3.5. Standards p.59 6.3.6. Cola samples p.60 6.3.7. Spiking p.60 6.3.8. Buffer p.61 Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 4 of 4 7. CALCULATIONS OF ANALYTICAL PARAMETERS ON HPLC CHROMATOGRAM p.62 7.1. RETENTION TIME, VOID TIME & RETENTION FACTOR p.62 7.2. VOLUMES p.62 7.3. SELECTIVITY p.63 7.4. COLUMN EFFICIENCY p.63 7.5. HETP p.63 7.6. RESOLUTION p.63 7.7. ASYMMETRY & TAILING FACTOR p.64 8. STATISTICAL ANALYSIS OF RESULTS p.65 8.1. STANDARD CURVE p.65 8.2. REPEATABILITY & REPRODUCIBILITY p.68 8.3. PRECISION p.75 8.4. SPIKING p.78 8.5. COLA SAMPLES p.81 9. DISCUSSION p.86 10. CONCLUSION p.88 11. SOURCES p.90 12. ANNEX p.92 Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 5 of 5 FIGURE LIST Figure 1.1: Structure of aspartame and its three main components Figure 1.2: Decomposition of aspartame in L-aspartic acid and L-phenylalanine Figure 1.3: Molecular structure and pk a values of aspartame Figure 2.1: HPLC main components Figure 2.2: Schematic diagrams depicting separation modes Figure 2.3: A chromatogram showing retention time (tR), void time (tM), peak width (wb), and peak height (h) Figure 2.4: Retention map and chromatograms of two basic antidepressants using mobile phases at various pH with percentage organic modifier being kept constant Figure 2.5: Diagrams showing two closely eluting peaks at various resolution values Figure 2.6: Graph illustrating the effects of α, k, and N on resolution Figure 2.7: A diagram showing the calculation of peak asymmetry (A s ) and tailing factor (T f ) from peak width at 5% height (W 0.05 ) according to the USP Figure 3.1: The typical graph of the normal distribution Figure 3.2: Normal quantile plot Figure 3.3: t-distribution compared to the normal distribution Figure 3.4: An F-distribution, showing how the degrees of freedom change the graph appearance Figure 3.5: An example of a scatter plot of data showing a linear correlation Figure 3.6: an example of a linear regression plot showing the vertical deviations Figure 3.7: the interpretation of the correlation coefficient Figure 3.8: A residual plot showing the ideal situation Figure 3.9: A boxplot showing the median and quartiles Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 6 of 6 Figure 4.1: Differences between linearity and non-linearity ranges Figure 4.2: Differences between precision and accuracy Figure 5.1: Steps for HPLC method development Figure 6.1: Chromatogram of the preliminary test Figure 6.2: Chromatogram of the standard solution. Figure 6.3: Aspartame supplied by Superco Analytical Figure 6.4: HPLC Agilent 1100 series Figure 6.5: Analytic scale Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 7 of 7 TABLE LIST Table 1.1: “Directive 94/35/EC - sweeteners for the use in foodstuffs” Table 2.1: Common HPLC Solvents and Their Properties Table 5.1: HPLC pump setup Table 5.2: Experimental conditions for the HPLC separation Table 6.1: Mobile phase method program Table 6.2: Description of the standard solutions Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 8 of 8 Resume Dette projekt handler om at bestemme indholdet af aspartam i forskellige colaprodukter ved hjælp af High Pressure Liquid Chromatography (HPLC). Der undersøges fire forskellige mærker; Coca-Cola Zero, Coca-Cola Light, Pepsi Max og Harboe cola Minus. Der er skrevet teori om aspartam, miljø og lovgivning for stoffet. Derudover er der lavet et teoretisk afsnit omkring HPLC og statistik. I laboratoriet fremstilles en metode til undersøgelse af aspartam i colaprodukter. Denne metode benyttes til at indsamle data for de forskellige fabrikater, som undersøges ved hjælp af forskellige statistiske parametre. I metodeudviklingen bliver det fundet, at aspartam kan adskilles fuldt fra de øvrige indholdsstoffer i colaprodukterne. Aspartamindholdet er bekræftet ved hjælp af et certificeret standardstof. I laboratoriet benyttes en Agilent HPLC med en C-18 kolonne, 150 mm længde med 5 µm partikeldiameter. Metoden benytter et gradientprogram med acetonitril og 22 mM fosfatbuffer pH 2,5 [31, s. 2]. Metoden bekræftes af statistiske beregninger, der viser at data for den samme cola er både repeterbart og reproducerbart. Gennem tests af nyere colaer af samme mærker, vises det at koncentrationen af aspartam for det samme mærke varierer signifikant fra flaske til flaske. Genfindingen på metoden vises at være tæt på 100 %, hvilket er yderst essentielt for metodens validitet. Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 9 of 9 Abstract The aim of this project is to determine the levels of aspartame in various cola products using High Pressure Liquid Chromatography (HPLC). We examine four different brands, Coca-Cola Zero, Coca-Cola Light, Pepsi Max and Harboe Cola Minus. There is written a section of theory about aspartame, the environment and legislation for the substance. Additionally, there is made a theoretical section on HPLC and statistics. In the laboratory, a method for the examination of the aspartame in the coke product is created. This method is used to collect data for the various fabricates which are examined using various statistical parameters. In method development, it is found that aspartame can be separated completely from the other ingredients of the cola products. Aspartame content is verified by means of a certified standard substance. In the laboratory an Agilent HPLC is used with a C-18 column, 150 mm long and a particle diameter of 5 micrometers. The method uses a gradient program of acetonitrile and 22 mM phosphate buffer pH 2.5 [31, p. 2]. The method is confirmed by statistical calculations that show that the data for the same cola is both repeatable and reproducible. Through tests of newer colas of the same brands, it is shown that the concentration of aspartame in the same brand vary significantly from bottle to bottle. The recovery of the method is close to 100 %, which is extremely essential for the validation of the method. Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 16 of 16 1.3. Objectives of study We would like to investigate the use of aspartame in soft drinks. To do this, we use HPLC to find the concentration of aspartame in different soft drinks. We would also like to look at a single product, and find the variance in the concentration of aspartame per drink. These tests would be done over several days. Besides finding what we previously described, we would like to validate, and perhaps improve, on a method for the HPLC for analyzing aspartame. 1.4. Legislation Aspartame has been authorised for use in soft drinks, foods and as a table-top sweetener by some Member States since the 1980s. The European legislation arranged its use in food production in 1994 following several safety evaluations carried on by the Scientific Committee on Food (SCF) in the years 1984 and 1988. Continuous reviews of the compound data were developed in 1997 and 2002 by the SCF. No danger concerns regarding possible developmental and reproductive toxicity, carcinogenicity or genotoxicity were found. Furthermore, in 2006 and in 2009 the Food Additives and Nutrient Sources added to food (ANS) and the Scientific Panels on Food Additives, Flavourings, Processing Aids and Materials in Contact with Food (AFC) evaluated two long-term carcinogenicity tests in multiple rats orally exposed to aspartame. This study was developed by the European Ramazzini Foundation (ERF) and in both investigations a quantitative doserelated growth of malignant tumours in female and male rats was reported. The ANS and AFC Panels determined that testing all the evidence available, there was no manifestation of any carcinogenic or genotoxic potential of the substance and there was no reason to update the Acceptable Daily Intake (ADI) for aspartame of 40mg/kg person body weight previously established. In a study published in 2010, the EU Member States asked National Experts to review the scientific data and literature about aspartame since 2002. They manifested that there was no necessity to reevaluate the previous opinions on the substance published by the SCF and the European Food Safety Authority (EFSA) Panels [5]. In 2010, two scientific articles were published, describing important injurious for health consequence of sweetener ingestion. The paper by Halldorsson [6] suggests a relation between a proliferated risk of preterm delivery and use of aspartame sweetened soft drinks. The publication by Soffritti [7] describes that aspartame is a risky carcinogenic agent in mice. Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 17 of 17 The EFSA informed the ANS that on February 2011, the European Commission requested EFSA for scientific assistance (according to Article 31 of Regulation (EC) No 178/2002) to start technical evaluation to check if the two previous mentioned publications should prompt a revision of the existing assumptions of EFSA related to the risk of artificial food additive sweeteners [8]. In May 2011, the European Commission asked EFSA to overtake the complete re-evaluation of the risks of aspartame to 2012. Already arranged for completion by 2020, the analysis of this sweetener is part of the efficient re-evaluation of all artificial food additives authorised by the EU organisms earlier to 20 January 2009, as assumed under Regulation EU 257/2010 [5]. Although all the controversy, the current legislation is: “Directive 94/35/EC - sweeteners for the use in foodstuffs” [9] and it is still using the following legal limits in soft drinks: Table 1.1: “Directive 94/35/EC - sweeteners for the use in foodstuffs” In Denmark the Ministry of Food, Agriculture and Fisheries (FVM) established the “positivliste” (eng: positivelist) which contains the limits of chemical substances that the food companies are allowed to use in their production. The legal limit of amount or concentration of the aspartame that is added to the food is set to be 600 mg/L [10] as in the rest of the European countries. So the food companies have to undergo these conditions and rules, so that the production of a product containing aspartame does have a concentration below 600 mg of aspartame pr. Liter product [11]. Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 18 of 18 2. HPLC theory HPLC, or High Pressure Liquid Chromatography, is a separations technique that is used in modern laboratory practice. Like the name, this method is a kind of a chromatography, where a sample is separated by using an eluent and a reference. But HPLC is a much more advanced chromatographic technique, which gives a more precise result, than the normal TLC plates. HPLC is not a very old technique, the first sign of chromatography was discovered by the Russian botanist Mikhail Tswett in the 1903 [12, p.3]. He separated plant pigments on chalk packed in glass columns. Since then the technique has been developed during time, and in 1952 the first chromatography machine was invented and was called the GC (Gas Chromatography). The discovery of this machine and its theoretical background was essential for the development of the LC (liquid Chromatography) technique. About 10 years later, the first High Performance Liquid chromatography machine was made. And during time improvement has made the machine more precise and better to use. 2.1. Advantages and disadvantages Using advanced machines like HPLC have advantages and limitation like every machine around the globe. It has an incredible precision and versatility, and these two factors make it special. HPLC can measure almost everything that can absorb UV-light or be ionized by mass spectrometric detection. And the measurement can be done with very good precision. But if the sample contains chemical substances that doesn’t absorb UV-light or cannot be ionized, then it’s problematic for the HPLC to make the measurement. HPLC has a very good detection limit, which can detect up to nano, pico and femtogram levels. It can also make measurements of up to 80 % of all existing chemical compounds, compared to the GC that can analyze around 15 %. 2.2. HPLC device The HPLC machine is divided into a column, pump, degasser and a valve. The column is made of metal or glass, and is used to press the mobile phase and the sample through it, with very high pressure. The degasser is used to remove gasses that are in the sample. Sometimes ultrasound is used if the machine doesn’t have a degasser. The valve is used to purge the machine, to remove chemicals. Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 19 of 19 Figure 2.1: HPLC main components. The sample the machine needs to analyze is separated in the machine by a distribution of its analytes in two different phases, and known as the mobile and stationary phase. These two phases have two different polarities, and attracts different analytes that are in the sample. The mobile phase is a liquid, and the stationary phase is sorbents packed inside the column. There are many different organic solvents that could be used as the mobile phase, such like hexane that is a very unpolar organic solvent. The stationary phase could for example be porous silica particles packed inside the column. The separation simply happens in the column (packed with sorbents) where the mobile phase is pumped inside the column at high pressure. The analytes will then interact with the phase with the same polarity as their own. The following picture explains how this works: Figure 2.2: Schematic diagrams depicting separation modes of (a) normal-phase chromatography (NPC) and (b) reversed-phase chromatography (RPC). [12,p.6] Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 20 of 20 The figure shows two different flows of the same sample, which contains polar and non-polar components. The figure to the left shows the interaction between the polar “silanol” inside the column, and the polar component. The non-polar component will just pass on with the flow without any interaction. The figure to the right is like the one to the left, but the interaction here happens with the non-polar phase and non-polar components. The polar components pass through the column with the flow. 2.3. Separations Modes There are different kinds of separations modes for the HPLC. Each separation has its own name, and is named after the purpose it is used for. The modes are: - NPC (Normal Phase Chromatography) - RPC (Reversed Phase Chromatography) - IEC (Ion Exchange Chromatography) - SEC (Size Exclusion Chromatography) The most common modes that are used when running HPLC, are NPC and RPC. NPC is a separation mode based on the adsorption and desorption of the analytes in the chemical sample, with the polar stationary phase. The mobile phase is here a nonpolar organic compound. This type of chromatography is used when the analytes are nonpolar, because they elute first with the mobile phase, and then the polar analytes elutes slowly after, because of their interaction with the polar phase. The RPC is the reversed or opposite mode of the NPC. The mobile phase is a polar compound and the stationary phase is an organic nonpolar compound. The mobile phase could be water, methanol or acetonitrile (ACN). The stationary phase is solid particles that are covered with a long chained organic and nonpolar compound. This kind of separation mode is used for polar analytes and is the most popular mode that is used in more than 80 % of all HPLC analyses [12, p.7]. IEC is a separation mode based on the exchange of ions. The stationary phase is typically cationic, where the mobile phase is anionic [12, p.7]. Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 21 of 21 SEC is also a kind of HPLC analysis, which is based on the molecular size of the particle, where the large particles migrate quickly, while small particles penetrate through the pores and migrates slowly through the column [12, p.9]. 2.4. Retention time & Void time The result of a HPLC analysis is a chromatogram. The chromatograms have on the x-axis the time it takes for the analytes to be detected and the absorbance on the y-axis. When a sample has been injected, the time between the injection and the top of a peak is called the retention time(t R ) . The “dead time” (retention time in the mobile phase), or the void time (t M ), is the first peak, or also called the first baseline disturbance by the sample [12, p.17]. The adjusted retention time (t’ R ) is calculated by substract the retention time from the void time: The adjusted retention time is the time, the sample remains in the stationary phase. A chromatogram from a HPLC analysis illustrates how to find these times: Figure 2.3: A chromatogram showing retention time (tR), void time (tM), peak width (wb), and peak height (h) [12, p.17]. Where W b is the width of the peak and h is the peak height. Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 22 of 22 2.5. Volumes There are different kinds of volumes, during analysis of chromatograms; retention volume (V R ), Void volume (V M ) and the peak volume. The retention volume, describes the volume required of the mobile phase to elute the sample analyte, at a particular flowrate (F): The void volume is the total amount of the mobile phase contained in the column. The void volume can be estimated by 3 different equation: Where: V c = Volume of empty column r = inner radius of column L = length of the column The peak volume is the volume of mobile phase containing the eluted peak: The peak volume can also be calculated by using the equation that contains the number of theoretical plates (N) and retention factor (k). The definitions of theoretical plate number and retention factor will be explained further during this section. 2.6. Retention factor (k) & partition coefficient (K) The degree of retention of the sample in the column is called the retention factor. It is defined as k, and is the time difference between the adjusted retention time (t’ R ) and the retention time (t M ): The k value decides if the component is retained or unretained in the stationary phase. Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 23 of 23 k=0 it is unretained k>20 it is retained Usually the k value in most analyses is between 1 and 20. The distribution, or the different between the concentration of the analytes in the stationary and mobile phase, is described by the partition coefficient K, and is estimated by dividing these two concentrations: Where [X s ] = concentration of analytes in the stationary phase [X m ] = concentration of analytes in the mobile phase 2.7. Selectivity (α) & Solvent strength The selectivity or the separation factor is the ratio or difference between two retention factors. For a good peak separation, the selectivity must be >1. A change in the stationary phase, and the composition of the mobile phase, affect the value of the partition coefficient K. Variations affect the selectivity too, because a change in the phases means a change of the retention time and the retention factors. The solvent strength refers to the capability of a chemical substance to elute analytes through a column. The strength of chemicals used in HPLC was defined by Hilderbrand and are listed in a scale called the hilderbrands elution strength scale (E 0 ): Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 24 of 24 Table 2.1: Common HPLC Solvents and Their Properties [12, p.27] Solvent strength is associated with the polarity of the solvents. In NPC (normal phase chromatography) the nonpolar compound hexane is a weak solvent, because NPC have a polar stationary phase. The opposite is true in RPC, because the stationary phase is a nonpolar compound. An increasing of the solvent strength will decrease the retention time (t R ), the retention factor (k), the selectivity (α) and the resolution (R s ). 2.8. Buffers In some analyses the modification of the pH of the mobile phase is required, if the analytes will elute through the column. Ionized form of analytes doesn’t partition very well with the nonpolar stationary phase in RPLC, and it has therefor a lower k-value, which means a lower retention time and bad separation of the peaks. An example is given from the book [12, p. 31] to explain the effect of the pH on the separation: Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 25 of 25 Figure 2.4: Retention map and chromatograms of two basic antidepressants using mobile phases at various pH with percentage organic modifier being kept constant. The diagram illustrates the importance of pH in the separation of basic analytes [12, p.31]. These two drugs ionize at two different pH-values. At pH = 2 there is no separation and therefor one peak is provided. A more basic condition about pH=8 gives a slightly good separation, but at pH=10 it’s a perfect separation. So the purpose with this example is to illustrate the importance of the pH on the separation of the analytes. 2.9. Column efficiency & number of plates The column efficiency depends on the number of plates in the column. A column with many plates is a very efficient column. An efficient column produces perfectly good and sharp peaks. The separation of the samples is also much better with increasing efficiency. The number of theoretical number plates (N) is defined by this equation: Where: σ = standard deviation of the peak 2.10. HETP (Height Equivalent to a Theoretical Plate) The distillation process from the industry was the first with the concept of a column with plate. A longer column would have an increasing number of plates and a good separations technique, to separates materials to many fractions of distillates. An HPLC column doesn’t really have plates, but it’s the same concept. The correlation between the column height and number of plates is described by this equation: Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 32 of 32 To calculate a probability using the normal distribution, special tables are used that contain values of a variable z; this value follows the modified version of the equation of the probability distribution, which is: The last part of the equation shows that F(z) is a cumulative probability [13, p. 126]. This means that a given value of z corresponds to a probability P that only increases as z increases. This equation pertains to a specific table that uses the standard normal distribution. In order to determine whether an amount of data is normally distributed, a standard quantile plot is used [13, p. 163]. This plot is a special graph, which effectively displays if all / some of the data differs from a normal distribution. For maximum assurance whether the data is normally distributed or not, it is best with at least 15-20 samples. To determine whether the data is normally distributed, all the measurements must be within the dotted lines. An example of a normal quantile plot is: 74 75 76 77 78 -1,64-1,28 -0,67 0,0 0,67 1,281,64 0,5 0,8 0,90,20,1 0,95 Normal Quantile Plot Figure 3.2: Normal quantile plot [15]. Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 33 of 33 3.3. t-distribution The t-distribution is very similar to normal distribution, inasmuch as the graphs of the two distributions are very much alike: Figure 3.3: t-distribution compared to the normal distribution [16]. The t-distribution, or student’s t-distribution, is symmetrical around the mean and bell-shaped like the normal distribution, but Figure 3.3 displays a function that is not found in the normal distribution; df, or degrees of freedom. The degrees of freedom, ν, are calculated via the formula [13, p. 187]: As can be seen on the graph, the lower the number of degrees of freedom, the wider the graph is. The higher the number of degrees of freedom, the more the t-distribution approaches the normal distribution. Hence, the t-distribution is a version of the normal distribution which allows for more variance when the number of samples, n, is low. It requires 30 samples or more for the t-distribution to become a good approximation to the normal distribution [13, p. 188]. Furthermore, the t-distribution allows for the use of the sample standard deviation, s, where the normal distribution does not. For a sample with a mean of and a standard deviation s, the random variable: Where µ is the population mean, follows the t-distribution. A table of data with values of probabilities for different values of t can be used to estimate the probability of a given sample mean in comparison to a Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 34 of 34 given population mean and sample standard deviation [13, p. 188]. This comes in handy when comparing different samples to each other, to see whether they share a similar mean or not. 3.4. F-distribution It is often assumed, when testing two different samples of size n 1 and size n 2 , that the variances equal each other. A problem could be to find the difference in these sample variances and to check whether they are similar to each other or not. This is an important factor to consider, when testing to see if two populations have the same variance. For two variances s 1 2 and s 2 2 with populations n 1 and n 2 respectively, the F-distribution has the random variable F [13, p. 190]: With the parameters, the degrees of freedom: To test whether two sample variances are different or similar, the F-value is calculated. This F-value pertains to a value on a graph: Figure 3.4: An F-distribution, showing how the degrees of freedom change to appearance of the graph [17]. The F-value corresponds to an area to the right on the graph which equals the probability of the two variances being the same. An F-value can be found in a special table, from which it can be pointed out by Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 35 of 35 using the degrees of freedom and the α-value (the confidence level). In this way, two hypotheses are tested: The F-value from the table can be compared to the F-value that is calculated. If the calculated value is bigger than the value obtained from the table, we can reject H 0 , also known as the null hypothesis. 3.5. Confidence interval The confidence interval is a statistic tool used to estimate the area where a specific population mean µ is located. The interval uses the sample mean and gives a lower and upper boundary for the real position of the population mean, with only little error. There are different values of the level of significance, and these indicate the probability that the true mean lies within the given boundary. The values that are typically used for the levels of significance are: - 95 % - 97.5 % - 99 % - 99.9 % The higher the level of significance chosen, the higher the chance that the real mean will be situated in the given area. Statistically, it can be formulated like: This can be rewritten to: Where the sample mean forms the basis for the interval of the real population mean, by creating an upper and lower limit [13, p. 209]. The value of z α is usually chosen amongst the values given above. This formula only applies for a sample amount of 30 and over, and uses the z-values from the normal distribution. It is also the population standard deviation that is in use. Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 36 of 36 It is possible to make another approximation and use the sample standard deviation s instead of the population standard deviation σ though, if the sample size is large. This leads to the formula [13, p. 210]: For a small sample of a normal population, the t-distribution can be used instead of the normal distribution, to provide more precise approximations: It is important to know that, for a level of significance of α, there is a (1-α) chance that the calculated interval misses the real value of the population mean. The interval is centered at and increases proportionally with the sample standard deviation [13, p. 211]. 3.6. Hypothesis Testing As mentioned in the in the section about the F-distribution, we use hypothesis testing to show whether there is a difference in a statistical value or not. It is important to have an objective method of looking at statistical values, such as means and variances, to determine whether there is a difference or not. The first step is to set up a hypothesis, consisting of a null hypothesis H 0 and an alternative hypothesis H 1 [13, p. 227]. The null hypothesis is the basis of the test; it is the hypothesis that the two parameters you are testing are not different from each other. The alternative hypothesis is the hypothesis that the two parameters are different; this can be expressed by a one-sided or a two-sided test. One-sided tests test whether the value of the parameter is either higher or lower than the parameter you are comparing it with. In the two-sided test, it is tested if the parameter is higher or lower than the parameter you are comparing it with, going either way. Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 37 of 37 If you are testing to see, whether a sample mean is equal to a true population mean, then the hypotheses could be [13, p. 230]: Null hypothesis: Alternative hypothesis: Reject null hypothesis if: H 0 : µ = µ 0 H 1 : µ < µ 0 Z < -z α H 1 : µ > µ 0 Z > z α H 1 : µ ≠ µ 0 Z < -z α/2 Or Z > z α/2 The test is performed by calculating a specific value of Z, which corresponds to an area on the graph of the standard normal distribution. This area gives the probability for the null hypothesis to be true. The formula is [13, p. 229]: Once the Z-value is calculated, it can be compared to the value in the tables for the standard normal distribution. Like with the confidence intervals, a level of significance is chosen. This normally falls on the same arbitrarily chosen values as the confidence intervals, like α = 0.05 or α = 0.01. Once you compare the two values, the one you calculated to the one you find from the level of significance, then you can decide whether to accept your null hypothesis or not. As can be seen on the table above, rejecting the null hypothesis or not depends of your choice of alternative hypothesis, which depends on the case. Like in most cases, if the population standard deviation σ is unknown, it can be substituted with the sample standard deviation s [13, p. 232]: This is for a sample size that is large though, (n > 30). If the sample size is small, and σ is unknown, the Z- value can be replaced by the t-value, assuming the population is normal [13, p. 233]: Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 38 of 38 This parameter follows the t-distribution, but the principle is the same as in the table shown before: Null hypothesis: Alternative hypothesis: Reject null hypothesis if: H 0 : µ = µ 0 H 1 : µ < µ 0 t < -t α H 1 : µ > µ 0 t > t α H 1 : µ ≠ µ 0 t < -t α/2 Or t > t α/2 Since the hypothesis test is based on a level of confidence of α, there is a probability of falsely rejecting the hypothesis, even though it is true. This probability corresponds to α. There are two types of errors [13, p. 227]: - Type I error: rejecting H 0 when H 0 is true - Type II error: Not rejecting H 0 when H 1 is true While α is the chance of committing a type I error, the chance to commit a type II error is defined by the letter β. The chance of committing a type II error is higher the lower the value of α is. For this reason, one should take care when choosing the value of α. It’s possible to calculate the chance that the sample mean is of the same or a higher value than the one already observed. This is called the P-value. The P-value is calculated by using the above formulas, and checking for the probability given at the Z- or t-value obtained from that. This would give an idea, whether or not the value of the sample mean is correct, or if there is a big probability that it would actually be of a different value. Comparing two different samples with each other to test whether the means are the same or not is hypothesis testing with two samples. For these two samples, some assumptions have to be made; both the samples need to be independent of each other, and have the means µ 1 and µ 2 and the variances σ 1 2 and σ 2 2 respectively. Also, the samples will be of size n 1 and n 2 . For a large sample, the statistic Z is approximately normal, and can be calculated by using the formula [13, p. 247]: Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 39 of 39 Where δ is the difference in the means µ 1 - µ 2 . A confidence interval can be calculated for the difference, in which the fixed value of the difference will be located with a probability of 1 – α [13, p. 247]: When doing a hypothesis test on two means from two independent samples, the null hypothesis is formulated as a difference in the means, as seen above. The difference can be set to a specific value, depending on how big a difference in the means one wants to test. It can also be set to zero, meaning that the test would be done to conclude if there is any difference at all. In general, the null hypothesis is [13, p. 248]: Where the difference is a specific value. The alternative hypothesis is similar to the alternative hypotheses of testing one mean; it can be both one-sided and two-sided, and is the hypothesis that the difference in the two means is either greater than, lower than or not equal to the specific value. For a large sample, the Z-value is calculated by the formula: In the table below, the hypotheses are shown [13, p. 249]: Null hypothesis: Alternative hypothesis: Reject null hypothesis if: H 0 : µ 1 - µ 2 = δ 0 H 1 : µ 1 - µ 2 < δ 0 Z < -z α H 1 : µ 1 - µ 2 > δ 0 Z > z α H 1 : µ 1 - µ 2 ≠ δ 0 Z < -z α/2 Or Z > z α/2 For small samples, the t-distribution can once again be used. This requires that more assumptions be made; both the populations being tested must be normal, and that the standard deviations must have a common value [13, p. 251]. The formula for calculating the t-value is then [13, p. 252]: Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 40 of 40 Where the variance is estimated by using a pooled estimator; this is done by pooling the sums of the squared deviations of the two different samples. The estimator s p is thus calculated by: It is important to note that the degrees of freedom now are calculated by: Here, the hypotheses are [13, p. 253]: Null hypothesis: Alternative hypothesis: Reject null hypothesis if: H 0 : µ 1 - µ 2 = δ 0 H 1 : µ 1 - µ 2 < δ 0 t < -t α H 1 : µ 1 - µ 2 > δ 0 t > t α H 1 : µ 1 - µ 2 ≠ δ 0 t < -t α/2 Or t > t α/2 The confidence interval for the difference can also be calculated. This is also done using the pooled estimator: 3.7. Linear Regression The purpose of looking at linear regression from a statistical point of view is to be able to state objectively whether there is a correlation between a set of paired data. To do this, the method of least squares is used to find the best regression between paired data, which can then be analyzed by various means. The regression curve of a linear relationship is given as: Where Y is a random variable, said to be dependent on x, Y being the dependent variable, x being the independent variable. The two constants α and β denote the intersection and the slope respectively, while the random variable ε accounts for any possible error, or other unknown factors besides α and β that may affect Y [13, p. 302]. Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 41 of 41 In reality, a set of paired data would yield a graph, from which a linear regression curve would be constructed: Figure 3.5 (left): An example of a scatter plot of data showing a linear correlation. [18]. Figure 3.6 (right): an example of a linear regression plot showing the vertical deviations [19]. While Figure 3.5 shows a scatter plot of the data, Figure 3.6 gives a linear regression curve based on the method of least squares. This linear regression curve would go by the formula: Where the hat sign (^) shows that is an estimate of the real value y i from the data set, for a specific value of x i . The constants “a” and “b” are also estimates of α and β respectively. The error for each statistic in the data set is: The errors are also known as the residuals, and the purpose of the least squares method is then to reduce the residuals so that they are as small as possible. This is done by making sure the estimators a and b make the equation: As numerically minimal as possible [13, p. 303]. To calculate a and b from a set of paired data (x,y) with n observations, the sum of squares and sum of cross products are calculated like: Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 48 of 48 4.4. Precision Precision is the determination of the reproducibility of the full method (including analysis and sample preparation) under regular operating variables. Precision is calculated by utilizing the method to evaluate a sample for an enough number of times to get statistically correct results. Precision is then designated as the relative standard deviation (CV%): 4.5. Accuracy Accuracy expresses the deviation between the true value and the mean value found. It is calculated by implementing the method to samples containing known quantities of analyte. The samples have to be analysed against blank and standard solutions to guarantee the elimination of interferences. Accuracy is then determined from the test values as a percentage of the amount of analyte retrieved by the measurement. Figure 4.2: Differences between precision and accuracy [24]. Errors in determinations can be divided into two main categories: random errors and systematic errors. Systematic errors appear from traceable sources due to the operator, the instrument or the methodology, and affect both the precision and the accuracy of the determination. A random error affects only the precision, and is complicated to remove, because this error is the result of random variations in the obtained signal, due to noise and different factors. Random errors are equivalent to the root of the summation of the squares of each individual contribution. The imprecision of a method is often governed in the most imprecise step by the random errors. Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 49 of 49 4.6. Limit of detection (LOD) LOD Is the lowest concentration of a sample that is detectable under the experimental conditions. This limit is important for the evaluation of dosages containing low analyte levels and for impurity tests. It is normally related as the concentration producing a signal-to-noise ratio of 2:1 and is then ratified by analyzing a determinate number of samples near this relation with the following equation. Signal-to-noise ratio is calculated by: Where: H = height of the component peak. h = absolute value of the largest noise variation from the chromatogram baseline of a blank solution. 4.7. Limit of quantification (LOQ) LOQ is the lowest concentration value of analyte in a sample that can be calculated with satisfactory accuracy and precision. It is related as the concentration producing a signal-to-noise ratio of 10: 1 and is ratified by analyzing several samples near this relation. 4.8. Ruggedness Ruggedness is the grade of reproducibility of the results acquired by the analysis of exactly the same sample under different normal experiment conditions ie different laboratories, instruments, analysts, assay temperatures, reagents, different days, small variations in mobile phase, etc [26]. Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 50 of 50 5. Method Optimization The 3 essential components for any HPLC method are: base sample preparation, analysis of HPLC results and standardization (calculations). All these components have to been investigated during the development of the project in order to obtain the final method optimization [27]. Figure 5.1: Steps for HPLC method development [28]. 5.1. Initial Method This report was initially based in the article “Determination of aspartame and phenylalanine in diet soft drinks by high-performance liquid chromatography with direct spectroflourimetric detection”, from Wróbel, K., Wróbel, K., and accepted in 1996 in the Journal of Chromatography A 773. According to this method a standard curve was made, so it is possible to determine the concentrations of the samples [29, p.2]. The sample was prepared by degassing (removing the CO 2 gasses by ultrasonic bath) the soft drinks. The drinks were mixed 1:1 (1 mL to one mL) with a solution known as a Carrez solution. The mixture was then diluted with water to 25 mL, and centrifugated. The liquid phase was then diluted (1:1) in phosphate buffer solution containing 34 % acetonitrile and 4 % methanol, the solution was again centrifuged and then filtered. These samples were prepared with different types of soft drinks. A volume of 20 µL of the sample is injected. The mobile phase consists of 81 % phosphate buffer, 2 % methanol and 17 % acetonitrile. The pH is 4.3. A gradient program is used: 0-1 min: 0.7 mL/min. 1-2 min: 1 mL/min. 2-8 min: 1 mL/min. [30, p.2579, p.2589]. Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 51 of 51 5.2. New Method Due to the long time required to prepare the samples using the previous method, a new and optimized method for the analysis of Aspartame with HPLC has been found during the research of this project. With shorter sample time preparation, the preparation errors are decreased and the statistical variables improved. This method optimization is based on the article “Direct HPLC-UV determination of cyclamate, saccharine and aspartame from soft drinks” from M.D. Croitoru, I. Fülöp, M. Kincses Ajtay, C. Balogh and M.T. Dogaru accepted in September 2011 [31, p.459-465]. In this article the following materials and methods are used: Equipment and reagents: • Merck HPLC system consisting of: quaternary pump L-7100, auto sampler L-7200, column thermostat L-7360, Diode Array Detector (DAD) L-7455, interface L-7000, solvent degasser L-7612 and HMS manager software; • LiChroCART 250-4 LiChrospher 100 RP-18 (5 μm) Merck column; • gradient grade acetonitrile (Merck); • aspartame p.a.; • purified water HPLC grade; • phosphoric acid, disodium phosphate, sodium hydroxide p.a. (Merck). HPLC Method: The mobile phase gradient and composition are shown in Table 5.1: Table 5.1: HPLC pump setup [31]. In the article, total analysis time was 24 min and sample volume was 100 μl. With a wavelenght of 196 nm the best chromatogram was extracted. Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 52 of 52 5.3. Optimized method Optimization was necessary because the laboratory provided a different column than the one from the article since that one was being used to perform other analysis. The one provided is a Phenomenex Luna C18 5µ 100A 150x4,60 mm mentioned before. This column is 15cm, shorter than the one used in the article with 18cm and it will allow obtaining a shorter retention time. Following the method explained in the “Method” section, using the mobile phase gradient and the HPLC configuration from the article and utilizing the column provided by the laboratory, a high and defined peak for the Aspartame was obtained. Due to these initial good results and the change in the column, a simple modification was required to perform an acceptable optimization. In order to improve the signal absorbance, the wavelength of the UV detector was changed from 196nm to 210nm, and the results were significantly better. The experimental conditions for the optimized HPLC aspartame separation are shown in the Table 5.2: Separation Variable Initial choice COLUMN Model Luna C18 (00F-4252-E0) Dimensions (length, I.d.) 150x4.60 mm Particle size 5 µm Stationary phase C-18 MOBILE PHASE Solvents A/B Buffer - ACN %-B Table 5.1 Buffer (pH, concentration) 2.5, 22 mM Flow rate 1.4 ml/min TEMPERATURE 25ºC pH 2.5 SAMPLE SIZE Volume 20 µl Table 5.2: Experimental conditions for the HPLC separation Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 53 of 53 5.4. Optimization results Due to the change in the length of the column, less retention time was obtained. Consequently, the necessary change in the wavelength of the UV detector allowed to obtaining a better absorbance. The method is robust in routine operation and usable by all the laboratories due to the rigour of the method standards and the statistics results. These data results are shown in the “Calculations of analytical parameters on HPLC chromatogram” and in the “Statistical data analysis” sections of the report. The repeatability of the chromatogram is confirmed, and there is enough time elapsed between samples for the column to reach the equilibrium with the new condition of the mobile phase. Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 54 of 54 6. Description of experimental work 6.1. Chromatograms The purpose of this experimental work in the laboratory is done to determine the amount of aspartame in light products. These products are soft drinks and we have focused on the most favorable cola products; Coca Cola Zero, Coca cola Light, Pepsi Max and Harboe Cola Minus. The method we use in the experimental work is from a scientific article found on Scifinder database. The specific manual or method can be found in the appendix. Safety, during an experimental work in a laboratory, is a very important issue. Therefore, the experimental work in the laboratory needs to be precise and carefully planned to obtain good results. To begin with we made some preliminary test of a diluted Coca cola Zero sample, to have an idea of the different peaks and retention times. By analyzing the sample we optain the following chromatogram: Figure 6.1: Chromatogram of the preliminary test. As we can see there are two major peaks with retention time 10 and 12 min, and there is a difference in the absorbance of the two measured wavelength, therefore we select the wavelength which gives the largest absorbance. A larger absorbance gives a better sensitivity, therefore we use the data,measured at 210 nm, in the following analysis. To determine between the two major peaks, we run a sample solution of pure aspartame. The standard solution has a concentration near 500 mg/L. We use the area of the first run to estimate the concentration Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 55 of 55 of the cola sample. We use the estimated concentration to be sure that the calibration curve covers the range of aspartame concentration in the cola samples. The first run of the standard solution of aspartame showed that aspartames retention time is around 12 minutes. Therefor we can define the retention time for aspartame to be near 12 minutes. The chromatogram of the first aspartame standard run: Figure 6.2: Chromatogram of the standard solution. 6.2. Materials HPLC HP Agilent 1100 series is used with Reverse Phase Chromatography (RPC) for the analysis of Aspartame. The detection device would be UV-PDA or UV-DAD. For the stationary phase, the column utilized is a Phenomenex Luna C18 5µ 100A 150x4,60 mm. Aspartame was supplied by Superco Analytical and the buffer solution compounds by the SDU laboratories. For the practical work in the laboratory, we used the following chemicals: Acetonitrile HiPerSolv CHROMANORM For HPLC Supergradient Batch:12B027806 Company: VWR Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 56 of 56 Hydrochloric Acid fuming 37 % For analysis Batch: 1723711 Company: Merck KGaA Ortho-phosphoricacid 85 % GR for analysis Batch: 1715164 Natriumdihydrogenphosphat monohydrat Pro analysis Batch: A674146 Company: Merck KGaA SodiumHydroxide 32% AnalaR NORMAPUR Batch: 11K170502 Company VWR Aspartame 99 % Production date: February 2012 Packed from: R474775 Lot nr. : LB64940 Highly filtrated Water Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 57 of 57 Figure 6.3 (left): Aspartame supplied by Superco Analytical. Figure 6.4 (right): HPLC Agilent 1100 series. 6.3. Method description The method we use is based on measuring the concentration of aspartame in a range of 0-500 mg /L. The analysis is performed by using the HPLC with a reversed phase chromatography. The mobile phase that is used is a mixture of two chemical substances, which are Acetonitrile and phosphate buffer, in a gradient program. The program is illustrated schematically in the Table 6.1: Time (min) 22 mM phosphate buffer pH 2.5 Acetonitrile Flow rate (mL/min) 0 93 7 1.400 8 93 7 1.400 8.1 85 15 1.400 18 85 15 1.400 18.1 93 7 1.400 Table 6.1: Mobile phase method program. Aspartame is detected by using a UV-detector (Diode Array Detector), and in the method from the scientific article they used a wavelength on 196 nm. But this wavelength seemed to be low, because acetonitrile can absorb with this specific wavelength. Therefor we chose to measure at two different wavelengths, one at 196 nm and 210 nm. We achieved the best absorbance at 210 nm, therefor we chose that wavelength in all further analyses. Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 64 of 64 So that indicates a very good resolution, and the two peaks are completely separated. 7.7. Asymmetry (A s ) & tailing factor(T f ) To calculate the tailing factor and asymmetry factor, we need to know the value of A, B, W 0.05 and f. These values are measured to be: A = 0.8 mm B =0.8 mm W 0.05 = 1.85 mm f=2 The T f value is under 1.0, so the peak doesn’t tailing or fronting. That indicates no asymmetry, so the peaks have a Gaussian peak shape with good symmetry. These calculated parameters have shown us that the method has a good separation of the different peaks. The resolution value is bigger than 2, so therefore we can conclude that the peaks are completely separated from each other. The efficiency of the column is very high because of the large number of theoretical plates in the column. This means that the method and the column easily can separate the components in the samples from each other. The peaks symmetry seems to be very good because the asymmetry factor is close to 1, and the tailing factor is close to 0. Which indicates that the peak shape is following the Gaussian peak shape, with perfect symmetry. Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 65 of 65 8. Statistical analysis of results 8.1. Standard curve For each standard solution created, three measurements of peak areas are made. Including three measurements at zero to prove that there is no measurement of aspartame at a concentration of zero, the results are: Concentration [mg/L] Area [mAU*s] Concentration [mg/L] Area [mAU*s] 0 0 200 6060,07 0 0 200 6072,01 0 0 200 6099,92 50 1515,64 300 8935,52 50 1527,02 300 8802,61 50 1513,77 300 8970,02 100 3048,2 500 14348,6 100 3036,82 500 14341,9 100 3049,83 500 14151,9 Mean 191,67 5637,44 Where the mean of the two columns are given in the end of the table. Note that the table (which is from Microsoft Excel) uses comma instead of dots to separate the integers from the decimals. The means are calculated using: The concentration is the independent variable, whereas the peak area is the dependent variable. We can calculate the values of S xx , S yy and S xy , from which all the statistical parameters can be calculated: From these, the values of a and b are found: Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 66 of 66 The error of sum of squares is also calculated: It is now possible to estimate the variance σ 2 : From this variance, the confidence intervals of α and β can be found: Where t α/2 is for n-2 degrees of freedom, from [13, p. 516]. It is also possible to find the coefficient of correlation: The value of R 2 can also be found: Excel gives the following graph of the standard curve: Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 67 of 67 With the residuals and normal quantile plot: The residuals do not look random. This is most likely because the standard curve is not entirely linear in the tested area – there is a tendency for the curve to straighten out at higher concentrations. This is also what can be seen from the residual plot. The normal quantile plot appears to be linear. Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 68 of 68 8.2. Repeatability & reproducibility We check the repeatability and reproducibility by sampling a specific Coca Cola Zero nine times a day over two days. Samples are made so that we, in total, obtain 18 samples from six different sample preparations (not different in the way that the methods are different). The results are shown in the table below, along with the calculated concentrations of the samples: Zero tests, first day Area [mAU*s] Concentration [mg/L] Concentration in cola [mg/L] 1,1 2271,98 74,05 370,26 1,2 2267,20 73,88 369,42 1,3 2264,23 73,78 368,91 2,1 2282,38 74,42 372,08 2,2 2353,22 76,89 384,45 2,3 2354,42 76,93 384,66 3,1 2374,42 77,63 388,16 3,2 2375,90 77,68 388,42 3,3 2370,88 77,51 387,54 Zero tests, second day Area [mAU*s] Concentration [mg/L] Concentration in cola [mg/L] 1,1 2381,67 77,89 389,43 1,2 2393,47 78,30 391,49 1,3 2385,58 78,02 390,11 2,1 2389,31 78,15 390,76 2,2 2380,72 77,85 389,26 2,3 2384,88 78,00 389,99 3,1 2291,11 74,72 373,60 3,2 2305,66 75,23 376,14 3,3 2300,1 75,03 375,17 Total mean (both days) 2340,40 76,44 382,21 Here, the different sample preparations are given as 1, 2 and 3 for each day, while each sample from each of the different preparations have been numbered 1, 2 and 3 as well. The concentration is calculated by using the formula obtained from the standard curve: The first sample of the first day: Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 69 of 69 As the samples have been diluted five times, a column with the actual concentration in the cola has been added to the table: We can use a t-test to determine whether the means measured over the two days are similar to each other. That is, we can test to see whether they come from the same population. We have two sets of data (n=9 in both cases), all coming from different sample preparations as well. For each, there is a mean and a standard deviation: We set up the following hypotheses for the test: The t-value is then calculated by first finding the pooled standard deviation: For the degrees of freedom: First day, cola concentration [mg/L] Second day, cola concentration [mg/L] 389,43 370,26 391,49 369,42 390,11 368,91 390,76 372,08 389,26 384,45 389,99 384,66 373,60 388,16 376,14 388,42 375,17 387,54 Mean: 385,11 379,32 Standard deviation: 7,655 8,834 Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 70 of 70 We find a t-value of: For a level of significance of α=0.05, and a two sided test, we fail to reject the null hypothesis, meaning that the two sets of data have the same means. This means that we can say with 95 % confidence that we can reproduce data so that it has the same mean. As the two data sets come from the same cola, this of course only goes for the same cola. As stated earlier, we will also test new colas. We will now look at the deviations that come from the different factors tested. As mentioned, we made 9 samples one day with three different sample preparations, and 9 samples the next day, also with three different sample preparations. This gives us different variances that can be considered: - Variance between repetitions, created by the machine - Variance between sample preparations, created by human error - Variance between different days, created by difference in the laboratory conditions (person, weather, chemicals etc.) Using SAS JMP, we test the variance of each of these different parameters. First, we test the machine variance for each day, and for each of the three sample preparations each day: First day Sample preparation 1 Sample preparation 2 370 375 380 385 390 370 375 380 385 390 Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 71 of 71 370 375 380 385 390 Sample preparation 3 Second day Sample preparation 1 Sample preparation 2 Sample preparation 3 The means and standard deviations can be seen in the table below: 375 380 385 390 375 380 385 390 375 380 385 390 Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 72 of 72 First day Second day Sample prep. 1 Sample prep. 2 Sample prep. 3 Sample prep. 1 Sample prep. 2 Sample prep. 3 Mean 369.53 380.40 388.04 390.34 390.00 374.97 Standard deviation 0.6817 7.203 0.4521 1.050 0.7501 1.282 It can be seen that the different sample preparations differ a lot in the obtained means, even though they are supposed to give the exact same means. Specifically, the 2 nd sample preparation of the first day has some error to it – the standard deviation is way out of scale, and should not be considered as normal. However, the table gives a good idea of the standard deviation of the machine. Differences in the mean are most likely caused by differences in the method preparation. We can also look at the standard deviation of the entire day, including both the deviation from the machine and the deviation from the different sample preparations. The data for each day is again put into SAS JMP, which gives the standard deviations: First day Second day 370 375 380 385 390 370 375 380 385 390 Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 73 of 73 The data for the graphs are given in the table below: First day Second day Mean 379.32 385.11 Standard deviation 8.833 7.657 If we eliminate the variation from the apparatus by taking the means of the three different sample preparations of each day, then we get the standard deviation of the sample preparations: First day Second day Sample preparation 1 369,53 390,34 Sample preparation 2 380,40 390,00 Sample preparation 3 388,04 374,97 Standard deviation 9,302 8,777 It can be seen that these standard deviations are higher. This is because the low deviation of the apparatus is no longer counted as a part of the total standard deviation. Between the days, the standard deviation can be calculated as the standard deviation of the means of the two days as given in the table at the top of the page: First day 379.32 Second day 385.11 Standard deviation 4.089 Here it can be seen, that the standard deviation between the two days are lower than between the different sample preparations. On the next page, we show all the standard deviations as CV% in a table. The CV% is calculated using: Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 80 of 80 Spike 2 Area [mAU*s] Concentration [mg/L] Expected concentration [mg/L] Difference Recovery [%] 1 6963,42 238,00 230,37 7,63 103,3 2 6991,56 238,99 230,37 8,62 103,7 3 6991,48 238,98 230,37 8,61 103,7 4 7008,79 239,59 230,37 9,22 104,0 5 7010,77 239,66 230,37 9,29 104,0 Mean: 6993,20 239,04 230,37 8,67 103,8 Standard deviation: 0,66405 0,28825 As mentioned earlier, we expect the unspiked Coca Cola Zero to have a mean concentration of ca. µ=76.44 mg/L. As we can see from the table of spike 0, we find a mean of 102.1 % of what we expected to find. We can then expect to find more in the spike 1 and spike 2 samples as well, so that the ideal recovery from these also would be at a few percentages higher than 100. We can now find the mean of the recovery from both spike 1 and spike 2 combined, and the standard deviation of these samples. We can also calculate the CV% to give a better idea of the deviation: Recovery [%] 103,74 103,38 103,44 103,33 103,32 103,31 103,74 103,74 104,00 104,03 Mean 103,60 Standard deviation 0,2819 CV% 0,2721 Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 81 of 81 So we end up with a mean recovery of 103.60 %, which means that this is what can be expected for future attempts of spiking. As mentioned, there was also minor increase in the amount measured in relation to the amount expected in the spike 0 tests. It might be possible that this increase also affects spike 1 and spike 2, even though we cannot confirm this. We have a CV% of 0.27 %, and this corresponds to the variation that can be expected if more tests were made. It is also important to remember, that the cola we use for spiking is diluted by a factor of 5 before being spiked. 8.5. Cola samples So far, we have only looked at the tests of a single type of cola from the same bottle. We also tested three other brands of colas, with the purpose of finding out whether the aspartame contents in these matched each other or not. Furthermore, we tested the same four brands of cola once again, this time from new bottles, to see whether the contents also differ from bottle to bottle, instead of just from brand to brand. The resulting concentrations found are listed in the table below. We start by analyzing Pepsi Max: Old Pepsi Max New Pepsi Max Area [mAU*s] Concentration [mg/L] Real concentration [mg/L] Area [mAU*s] Concentration [mg/L] Real concentration [mg/L] 3523,89 117,80 589,01 3340,15 111,38 556,91 3529,47 118,00 589,99 3353,32 111,84 559,21 3526,22 117,88 589,42 3355,32 111,91 559,56 Immediately, it is possible to see a difference between the measured concentrations in the new and old Pepsi Max’s. We want to test the means by using a t-test, so we start by setting up a null hypothesis and an alternative hypothesis: Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 82 of 82 We then input the data in SAS JMP, and run a t-test: From the graphics, it is possible to see that the two means are different, based on their low variance. We now set up a table of data from the t-test: Old Pepsi Max New Pepsi Max Mean 589.47 558.56 Standard deviation 0.4922 1.440 t-test data t-ratio -35.193 Prop > |t| 0.0002 The parameter “Prop > |t|” gives the probability for the t-ratio to be of the same or a more extreme value, provided we assume the null hypothesis is correct. If this value is lower than the value of our chosen level of significance, then we can reject the null hypothesis. With 99 % confidence, this null hypothesis can easily be rejected. So we conclude that the two means are different, meaning that there is a significant difference in the concentrations of the different colas. 555 560 565 570 575 580 585 590 595 Column 1 1 2 Column 2 -40 -30 -20 -10 0 10 20 30 40 Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 83 of 83 We then look at Coca Cola Light: Old Coca Cola Light New Coca Cola Light Area [mAU*s] Concentration [mg/L] Real concentration [mg/L] Area [mAU*s] Concentration [mg/L] Real concentration [mg/L] 1080,25 32,40 162,02 1394,69 43,39 216,97 1158,21 35,13 175,64 1400,25 43,59 217,94 1083,25 32,51 162,55 1401,8 43,64 218,21 With the same hypothesis, we also test whether the means here are similar or not: Old Coca Cola Light New Coca Cola Light Mean 166.74 217.71 Standard deviation 7.715 0.6521 t-test data t-ratio 11.402 Prop > |t| 0.0072 The probability for the t-ratio is higher this time, but can still be rejected with 98 % confidence. We also test Harboe Minus: Old Harboe Minus New Harboe Minus Area [mAU*s] Concentration [mg/L] Real concentration [mg/L] Area [mAU*s] Concentration [mg/L] Real concentration [mg/L] 1744,58 55,62 278,10 1872,15 60,08 300,39 1742,75 55,56 277,78 1920,31 61,76 308,81 1722,39 54,85 274,23 1912,56 61,49 307,46 -60 -40 -20 0 102030405060 160 170 180 190 200 210 220 Column 1 1 2 Column 2 Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 84 of 84 Results of the t-test: Old Harboe Minus New Harboe Minus Mean 276.70 305.55 Standard deviation 2.148 2.611 t-test data t-ratio 9.981 Prop > |t| 0.0026 We see higher standard deviations for this brand of cola. However, the null hypothesis can still be rejected with 99 % confidence. Lastly, we can look at Coca Cola Zero. As we did a lot of tests on the first Coca Cola Zero we had, we randomly choose a set of three data points from the same sample preparation to compare with the three data points from the new Coca Cola Zero. We then proceed with t-testing in the same way as the above three brands: Old Coca Cola Zero New Coca Cola Zero Area [mAU*s] Concentration [mg/L] Real concentration [mg/L] Area [mAU*s] Concentration [mg/L] Real concentration [mg/L] 2374,42 77,63 388,16 2367,84 77,40 387,01 2375,9 77,68 388,42 2362,70 77,22 386,11 2370,88 77,51 387,54 2363,57 77,25 386,26 -40 -30 -20 -10 0 10 20 30 40 270 275 280 285 290 295 300 305 310 Column 1 1 2 Column 2 Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 85 of 85 386 386,5 387 387,5 388 388,5 Column 1 1 2 Column 2 -2,0-1,5-1,0-0,5 0,0 0,5 1,0 1,5 2,0 t-test: Old Coca Cola Zero New Coca Cola Zero Mean 388.04 386.46 Standard deviation 0.4521 0.4822 t-test data t-ratio -4.140 Prop > |t| 0.0145 Here, we can reject the null hypothesis with 95 % confidence. As we showed in the repeatability and reproducibility, it is possible to say that two samples from the same cola will give the same results. However, we can conclude for all of the four tested cola brands that there is a difference in the concentrations of aspartame between production dates. Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 86 of 86 9. Discussion The aim of the project was to find a method with which we could find the concentration of aspartame in soft drinks. We wanted to be able to separate aspartame from the other components in the cola via HPLC analysis, which we would accomplish by changing different analysis parameters. We based our analysis on a method from a scientific article. At first, we ran several samples of different cola brands to get an idea about the levels of aspartame present in the colas. Afterwards, we ran a standard solution to check what retention we could expect aspartame to have under the chosen conditions. It is a good idea to try to determine the concentration range we can expect to see our cola samples in, by running a few samples once the details of the method have been confirmed by good chromatograms that meet the requirements. From these samples, we can determine the range in which we need the concentrations of our standard solutions to be. The retention time of aspartame in all the samples highly depends on the buffer; this can be the pH of the buffer, or the contents of the buffer other than the bases/acids. We have been very careful in the laboratory with preparing the buffer, to avoid having these changes in the retention time. The change in retention time could also be caused by other unknown factors. We used a shorter column than the one given in the article, since we had to share the HPLC with another group. This meant that we had to find a column that both groups could use. This did not seem to affect our results in a negative way, but seemed to give us an acceptable separation of the different components of the soft drinks and a shorter retention time of aspartame. We use another wavelength than given in the article, with which we achieve a higher absorbance, meaning that the results are more reliable. We achieved separation of the wanted products, but the resolution of aspartame in relation to the nearest peak was very high. Therefore, it would be an option to optimize the method even more. This could be done by changing the gradient flow, which could result in reduced analysis times. It would also be possible to run standards and test for the other component that appears strongly in every chromatogram; this component is believed to be another sweetener, and a simultaneous determination of two sweeteners would prove more useful. Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 87 of 87 Because of the limited time in the laboratory, we choose to keep the method as it is, and start the measurements. Since every time a change to the method is made, we would have to start all over with all analyses, and we do not want that. We found that the data is normally distributed, and we produced a standard curve with a range of 0-500 mg/L of aspartame, with good linearity. We find a coefficient of determination of 0.999, which is very satisfying. We then choose to use this standard curve to calibrate the concentration of all our future samples. To get an acceptable calibration curve, it is important to be very careful when preparing the samples in the laboratory. We measure each standard 3 times to be statistically sure that the data is useable. Since the standard curve does not go through (0,0) on the graph (even within the confidence intervals) there must be some error involved with the measurements. This could be caused by human error, a continuous error in the detector of the HPLC apparatus, or perhaps if the curve is not entirely linear. This last problem would cause the trendline to deviate from (0,0) if some of the other points are off course. From the ANOVA calculations, we can see that human error has a big influence on the sample preparations. This can also be caused by sample preparations done by different people. This might also have had an influence on the standard curve. We determined via a t-test that the method has both repeatability and reproducibility, but only for the same cola. As we tested over several sample preparations, and over two days, the method is valid for the same cola at any times. To calculate the recovery, we use the calibration curve to find the concentration of the spiked samples. We compared this to the expected concentrations and find a mean recovery of 103.60 %. This could be caused by several factors. A problem could be the variation in the calibration curve, along with error in the machine or human error, as described before. We tested cola samples from different bottles, and determined via t-tests that the difference from bottle to bottle of the same brand is significant. This would mean that the producers do not measure the exact amount put into every batch. In reality, this has no significance as long as the concentrations of aspartame stay under the legal limits. We found that there is a huge difference in the amount of aspartame between the different brands. In general, our repetitions have a very low standard deviation. This is the standard deviation of the machine. The standard deviation between the sample preparations is much higher, and this is caused by the human error. This proves that the machine is the most reliable part. Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 88 of 88 10. Conclusion Choice of method When we first started the project, we were looking at a method that included a long sample preparation. Unfortunately, long sample preparation are not only time demanding, but also provide a higher probability of human error in the laboratory. However, we later found a newer method that required less sample preparation, and we decided to use this method as a starting point for our own experimental work. We improved on the method based on what resources were available in the laboratory, and ended up with a solid method that we would then validate using statistics. The HPLC (high performance liquid chromatography) machine we use has the following specs: Merck HPLC system with quaternary pump L-7100, auto sampler L-7200, column thermostat L-7360, Diode Array Detector (DAD) L-7455, interface L-7000, solvent degasser L-7612 and HMS manager software LiChroCART 250-4 LiChrospher 100 RP-18 (5 μm) Merck column The method gave retention times for aspartame in the area of just over 12 minutes. In total, the cola samples were run for 30 minutes, with a post run of 5 minutes included to clear the column of any residuals. We observed perfect, Gaussian peaks for both aspartame and other UV-absorbing content of the cola samples. Analytical parameters We obtained the first chromatograms from our cola samples, and used these to calculate some of the most important parameters related to the chromatograms; retention times, selectivity, number of plates and resolution. We conclude that the yielded chromatograms have excellent plate numbers and resolution – for the selected chromatogram, the plate number (column efficiency) is 28535, giving an HETP (height equivalence of a theoretical plate) of 5.2566 µm. Furthermore, we calculated the resolution of the aspartame peak in same chromatogram in relation to the nearest large peak, and obtain a value of 27.5379. Based on the similarity of all the chromatograms, we conclude that these results can be transferred over to all of the aspartame peaks of the chromatograms we obtain during the entire project. Group 1 Determination of aspartame in soft drinks using HPLC K-PTE4 Page 89 of 89 Statistical parameters The standard curve was created from the data of the standard solutions, and resulted in a linear curve with a coefficient of determination of 0.999, and a linear range of about 0-500 mg/L of aspartame. From this curve, we obtained the equation used to calculate the concentration of all of our cola samples. With the parameters α and β (the intersection and the slope respectively), we got and . With the confidence intervals with α=0.05 also calculated, we can see that there is very little variation in the value of the slope of the curve. However, the confidence interval for the intersection is large, but does not contain the value 0 as it should have, which could be caused by several factors. We conclude that the method used has repeatability and reproducibility; by t-testing, we found that the concentration measured in the same cola was the same from one day to another, and between different sample preparations. We found the variance of the different aspects of the tests; the variance of the machine, the variance of the sample preparations and the variance between days. The precision of the method was tested by ANOVA, from which we can conclude that the precision of different sample preparations highly depends on the person performing the analysis. In the spiked samples, we find a percentage of recovery of 103.60 %. This is above the expected value of 100 %, and could be caused by error in the sample preparation. In the unspiked samples, we find 102.1 %, which backs up the above hypothesis that it could be caused by human error. For the 4 different cola brands tested, we conclude by t-test that the contents differ from bottle to bottle. The contents of the different colas can be seen below: Old Cola concentration [mg/L] (bottle 1) New Cola concentration [mg/L] (bottle 2) Coca Cola Zero 382.21 386.46 Coca Cola Light 166.74 217.70 Pepsi Max 589.47 558.56 Harboe Minus 276.70 305.55 The concentrations shown are for non-diluted cola samples. So all in all, we acquired the results we were after, and were able to develop a method that works for finding aspartame in soft drinks.